1. ## progression equation

Hi Friends,

Case A:

1, 3, 5, 7, 9.....
To find the Nth term for the above type of progression, the equation is:
Nth term = a + (n-1)d
where a = initial term
d = common difference
n = number of terms

Case B:

1, 2, 4, 7, 11, ....

My question is: Is there any general equation to find the Nth term for the above type of progression ?
Note that the common difference is variable but has a constant progressive rate i.e, 1,2,3,4,.... and iteself has a common difference of 1

Regards.

2. ## Re: progression equation

Case B: yes.

Note that

$a_1 = 1$
$a_2 = 1+1$
$a_3 = 1+1+2$
$a_4 = 1+1+2+3$
$a_n = 1+(1+2+...+(n-1))$

Therefore, $a_n = 1 + (1+2+...+(n-1)) = 1+\frac{(n-1)n}{2}$

3. ## Re: progression equation

Thank you very much richard1234.
That's perfect. Have a nice day.